Rewrite as a simplified fraction. ${0.80\overline{4} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 804.4444...\\ 100x &= 80.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 724}$ ${x = \dfrac{724}{900}} $ ${x = \dfrac{181}{225}} $